Algoritmos de aproximação para problemas de roteamento e conectividade com múltiplas funções de distância

Orientador: Lehilton Lelis Chaves PedrosaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Nesta dissertação, estudamos algumas generalizações de problemas clássicos de roteamento e conectividade cujas instâncias são compostas por um grafo completo e múltiplas funções de distância. Por exemplo, existe o Problema do Caixeiro Alugador (CaRS), no qual um viajante deseja visitar um conjunto de cidades alugando um ou mais carros disponíveis. Cada carro tem uma função de distância e uma taxa de retorno ao local do aluguel. CaRS é uma generalização do Problema do Caixeiro Viajante (TSP). Nós lidamos com esses problemas usando algoritmos de aproximação, que são algoritmos eficientes que produzem soluções com garantia de qualidade. Neste trabalho, são apresentadas duas abordagens, uma baseada em uma redução linear que preserva o fator de aproximação e outra baseada na construção de instâncias de dois problemas distintos. Os problemas considerados são o Steiner TSP, o Problema do Passeio com Coleta de Prêmios e o Problema da Floresta Restrita. Generalizamos cada um desses problemas considerando múltiplas funções de distância e, para cada um deles, apresentamos um algoritmo de aproximação com fator O(logn), onde n é o número de vértices (cidades). Essas aproximações são assintoticamente ótimas, já que não há algoritmos com fator o(log n), a não ser que P = NPAbstract: In this dissertation, we study some generalizations of classical routing and connectivity problems whose instances are composed of a complete graph and multiple distance functions. As an example, there is the Traveling Car Renter Problem (CaRS) in which a traveler wants to visit a set of cities by renting one or more available cars. Each car is associated to a distance function and a service fee to return to the rental location. CaRS is a generalization of the Traveling Salesman Problem (TSP). We deal with these problems using approximation algorithms which are efficient algorithms that produce solutions with quality guarantee. In this work, two approaches are presented, one based on a linear reduction that preserves the approximation factor and the other based on the construction of instances of two distinct problems. The studied problems are the Steiner TSP, the Profitable Tour Problem, and the Constrained Forest Problem. We generalize these problems by considering multiple distance functions and, for each of them, we present an O(log n)-approximation algorithm, where n is the number of vertices (cities). The factor is asymptotically optimal, since there is no approximation algorithm with factor o(log n) unless P = NPMestradoCiência da ComputaçãoMestra em Ciência da Computação001CAPE

A Hybrid Transgenetic Algorithm for the Prize Collecting Steiner Tree Problem

Evolutionary algorithms are effective search tools for tackling difficult optimization problems. In this paper an algorithm based on living processes where cooperation is the main evolutionary strategy is applied to the Prize Collecting Steiner Tree Problem, an NP-hard combinatorial optimization problem. The Transgenetic Algorithm presented here is hybridized with path-relinking. Computational results of an experiment performed with benchmark instances are reported. The results obtained for the Prize Collecting Steiner Tree Problem with the application of the hybrid Transgenetic Algorithm are compared with the results of three effective approaches presented previously. The computational experiment shows that the proposed approach is very competitive concerning both quality of solution and processing time

Diversity and Otherness

This book critically examines multiple ways in which cultural diversity is, and has been represented and handled. It questions the construction of differences in doing culture while emphasizing the fluidity of cultural entanglements. It is an invitation to re-think norms, practices and negotiations of diversity and otherness, to distinguish emancipatory from standardizing approaches and to “transculturalize” the study and the politics of culture

Diversity and Otherness

This book critically examines multiple ways in which cultural diversity is, and has been represented and handled. It questions the construction of differences in doing culture while emphasizing the fluidity of cultural entanglements. It is an invitation to re-think norms, practices and negotiations of diversity and otherness, to distinguish emancipatory from standardizing approaches and to “transculturalize” the study and the politics of culture